The Elephant in the Classroom: Helping Children Learn and Love Maths

 

Jo Boaler

Souvenir Press | 2009 | 288 páginas | rar - epub | 1,39 Mb

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"Help children to learn to love the subject... Make mathematics more the mathematics that people need out there in the world."BBC Radio 4's 'Woman's Hour'
Why do millions struggle with mathematics and what can teachers do to change that?
Jo Boaler has followed the progress of thousands of pupils in two countries (the UK and USA), monitoring how they learn maths through their school carers and then following them into adult life. This remarkable research is the foundation of her investigations into the impact that differing maths experiences can have on an entire generation. Jo Boaler outlines what has gone wrong, identifying the problems facing children in mathematics classrooms today and offers concrete solutions for parents and teachers that will revolutionise children's experiences with maths.
"A very interesting book which addresses some common problems found in the maths classroom which has been well researched and provides positive solutions and practical activities for those interested in trying to encourage students of today to become mathematicians of tomorrow."Times Educational Supplement online
The Elephant in the Maths Classroom offers concrete suggestions on ways to teach maths well, and ways to help children in the home, that will offer new and more effective ways of learning maths. This is an exciting way forward, a new approach that teaches children to reason and problem solve; helping all children, even those who think that they are maths failures and that they could never enjoy maths.
An indispensable guide and resource for parents, teachers and educationalists, that inspires and enthuses as much as it teaches.

Contents
Acknowledgements
Introduction: Understanding the Urgency
1 / What is maths? And why do we all need it?
2 / What’s going wrong in classrooms? Identifying the problems
3 / A vision for a better future: Effective classroom approaches
4 / Banishing the monsters: Moving to more effective forms of assessment
5 / Making ‘low ability’ children: How different forms of grouping can make or break children
6 / Paying the price for sugar and spice? How girls and women are kept out of maths and science
7 / Talking with Numbers: Key strategies and ways of working
8 / Giving children the best mathematical start in life: Activities and advice
9 / Making a difference through work with schools
Appendix

Livros da mesma autora:

What's math got to do with it? : helping children learn to love their most hated subject--and why it's important for America por Jo Boaler Idioma: Inglês   Editora: New York : Viking, 2008.

Experiencing school mathematics : traditional and reform approaches to teaching and their impact on student learning por Jo Boaler Idioma: Inglês   Editora: Mahwah, N.J. : L. Erlbaum, 2002.

Multiple perspectives on mathematics teaching and learning por Jo Boaler Idioma: Inglês   Editora: Westport, Conn. : Praeger, 2000.

Exploiting Mental Imagery with Computers in Mathematics Education

Rosamund Sutherland e John Mason

Springer | 1995 | 337 páginas | pdf |10 Mb

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The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Contents
Part 1. Emphasizing the External
Imagery for diagrams
Tommy Dreyfus
External representations in arithmetic problem solving
Giuliana Dettori and Enrica Lemut
Visualisation in mathematics and graphical mediators: an experience with 11-12 year old pupils
Angela Pesci
Visual organisers for formal mathematics
David Tall
Mediating mathematical action
Rosamund Sutherland
Mathematical objects, representations, and imagery
Willibald D6rjler
Part 2. Imagery in Support of Geometry
Images and concepts in geometrical reasoning
M. Alessandra Mariotti
Between drawing and figure
Reinhard Holzl
The functions of visualisation in learning geometry
Eric Love
Geometrical pictures: kinds of representation and specific processings 142
Raymond Duval
Part 3. Linking Screen and Mental Imagery 159
Overcoming physicality and the external present: cybernetic manipulatives 161
James J. Kaput
On visual and symbolic representations 178
Luis E. Moreno A. and Ana Isabel Sacristan R.
The dark side of the Moon 190
Richard Noss and Celia Hoyles
Ruminations about dynamic imagery (and a strong plea for research) 202
E. Paul Goldenberg
On designing screen images to generate mental images
Richard J. Phillips, John Gillespie, and Daniel Pead
Learning as embodied action .233
Stephen Campbell and A. J. (Sandy) Dawson
Part 4. Employing Imagery 251
The importance of mental perception when creating research pictures 252
Monique Sicard and Jean-Alain Marek
Random images on mental images
Mario Barra
Imagery as a tool to assist the teaching of algebra
Dave Hewitt
Mathematical screen metaphors
John Mason and Benedict Heal
Exploiting mental imaging: reflections of an artist on a mathematical excursion .
Stephen A.R. Scrivener
Index 323

International Perspectives on Gender and Mathematics Education

Helen J. Forgasz, Joanne Rossi Becker e Kyeong-Hwa Lee

Information Age Publishing | 2010 | 467 páginas | rar - pdf | 2,1 Mb

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A Volume in International Perspectives on Mathematics Education - Cognition, Equity & Society Series Editor Bharath Sriraman, The University of Montana and Lyn English, Queensland University of Technology Why a book on gender issues in mathematics in the 21st century? Several factors have influenced the undertaking of this project by the editors. First, an international volume focusing on gender and mathematics has not appeared since publication of papers emerging from the 1996 International Congress on Mathematical Education (Keitel, 1998). Surely it was time for an updated look at this critical area of mathematics education. Second, we have had lively discussion and working groups on gender issues at conferences of the International Group for the Psychology of Mathematics Education [PME] for the past four years, sessions at which stimulating and ground-breaking research has been discussed by participants from many different countries. Some publication seemed essential to share this new knowledge emerging from a wider variety of countries and from different cultural perspectives. Third, some western countries such as Australia and the USA have experienced in recent years a focus on the "boy problem," with an underlying assumption that issues of females and mathematics have been solved and are no longer worthy of interest. Thus it seemed timely to look more closely at the issue of gender and mathematics internationally. When the idea for this volume first emerged, invitations were issued to those regularly attending the working and discussion groups at PME. Potential authors were charged to focus on gender issues in mathematics and were given wide scope to hone in on the issues that were central to their own research efforts, or were in receipt or in need of close attention in their own national or regional contexts.

Contents
Section I History, Policy, and Non-School Factors
1 International Perspectives on Gender and Mathematics Education: An Overview...1
Joanne Rossi Becker, Helen Forgasz, Olof Bjorg Steinthorsdottir, and Kyeong-Hwa Lee
Section I History, Policy, and Non-School Factors
2 The Ladies’ Diary or Woman’s Almanack, 1704–1841..... 15
Teri Perl
3 Conversations of Parents and Children Working on Mathematics.... 33
Melfried Olson, Judith Olson, Claire Okazaki, and Thuy La
4 Out-of-School-Time (OST) Programs as Mathematics Support for Females.. 55
Lynda R. Wiest
5 Freedom to Choose?: Girls, Mathematics and the Gendered Construction of Mathematical Identity... 87
Fiona Walls
6 Gender Mainstreaming: Maintaining Attention on Gender Equality...111
Colleen Vale
Section II National Focus
7 Studies in Mexico on Gender and Mathematics...... 147
Sonia Ursini, Martha P. Ramírez, and Claudia Rodríguez, María Trigueros, and Ma. Dolores Lozano
8 Gender Differences When Working with Algebraic Variables: A Study with Mexican Secondary School Students.... 173
Carolina Rubí Real Ortega and Sonia Ursini
9 Factors Contributing to Gender Differences in Mathematics Performance of United States High School Students....203
Pamela L. Paek
10 Gender Differences in Mathematics Achievement: Evidence from Regional and International Student Assessments.... 225
Xin Ma
11 Mathematics Achievement in Icelandic Playschools: Examining When Gender Differences Emerge..... 249
Olof Bjorg Steinthorsdottir, Kimberly Dadisman, Dylan L. Robertson, and Kristjana Steinthorsdottir
12 Mathematics Teacher Education and Gender Effects... 263
Sigrid Blömeke and Gabriele Kaiser
Section III High Achievers
13 Discovering the Potential of Gifted Females in Mathematics.... 287
Kyeong-Hwa Lee, Eun-Jung Lee, Seoung-Hey Paik, and HeiSook Lee
14 Gender and High Achievers in Mathematics: Who and What Counts?.... 315
Gilah C. Leder and Helen J. Forgasz
15 What Are High Achieving Young Women’s Perceptions of Mathematics Over Time?.... 341
Amanda Lambertus, Susan Bracken, and Sarah Berenson
Section IV Tertiary Students
16 The Influence of High School and University Experiences on Women’s Pursuit of Undergraduate Mathematics Degrees in Canada......365
Jennifer Hall
17 Try and Catch the Wind: Women Who Do Doctorates at a Mature Stage in Their Lives.... 391
Ansie Harding, Leigh Wood, and Michelle Muchatuta With Barbara Edwards, Lucia Falzon, Sibba Gudlaugsdottir, Belinda Huntley, Jillian Knowles, Barbara Miller-Reilly,and Tobia Steyn
18 Recognizing Gender in Mathematics Relationships: A Relational Counseling Approach Helps Teachers and Students Overcome Damaging Perceptions..... 421
Jillian M. Knowles
Contributors.......451

Bringing the Common Core Math Standards to Life: Exemplary Practices From Middle Schools

Yvelyne Germain-McCarthy 

Routledge | 2014 | 247 páginas | rar - pdf | 2,94 Mb

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As middle school math teachers shift to the Common Core State Standards, the question remains: What do the standards actually look like in the classroom? This book answers that question by taking you inside of real, Common Core classrooms across the country. You’ll see how exemplary teachers are meeting the new requirements and engaging students in math. Through these detailed examples of effective instruction, you will uncover how to bring the standards to life in your own classroom!

Special Features:

• A clear explanation of the big shifts happening in the classroom as a result of the Common Core State Standards 
• Real examples of how exemplary teachers are meeting the CCSS by teaching problem solving for different learning styles, proportional reasoning, the Pythagorean theorem, measurements, and more
• A detailed analysis of each example to help you understand why it is effective and how you can try it with your own students
• Practical, ready-to-use tools you can take back to your classroom, including unit plans and classroom handouts

Learn Science, Learn Math, Learn to Teach Science and Math, Homo Sapiens!

Hedy Moscovici, Penny J. Gilmer e Katherine C. Wieseman

Sense Publishers | 2012 | páginas | rar - pdf | 2,9 Mb

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Dr. Hedy Moscovici's life on three continents and her battle with ovarian cancer shaped the unique co-learning and participative leadership perspective on science and mathematics education shared in this book. This text has multiple audiences - prospective and practicing teachers wanting to motivate their students to learn, science and mathematics educators mentoring teachers to become transformative intellectuals and critical pedagogues, parents interested in their children's advancement, and interested policymakers and public wishing to deepen their understanding about learning in general and educational issues in science and mathematics. Two mottos, "I can't learn from you if you can't learn from me" and "to teach is to learn twice," summarize the essence of her message. The spotlight is on the critical interdependence of factors, specifically human ability to construct understanding; necessity of disequilibrium to spark neural rewiring; cognition-emotion (pleasure vs. pain, even science or math phobia) connections; sociocultural context; dilemma created by the absence of a clearly trustworthy "learning meter" for a society valuing objective measurement of quality of learning; human relationships sustained by three R's (rights, responsibilities, respect); and, heightened awareness of power relationships leading to a spirit of collaboration, recognition of each individual's strengths and expertise; and critical pedagogy.

TABLE OF CONTENTS

Illustrations.............. ix

Dedication ................... xi

Acknowledgements ............ xiii

Abbreviations ............. xv

Foreword (by Katherine Wieseman and Penny J. Gilmer) ....... xvii

Chapter 1 Worldview as a Dynamic Entity ...... 1

Chapter 2 What Do You Mean, You Know Science and Mathematics? ..... 17

Chapter 3 Emotional and Intellectual Involvement While Learning Science and Mathematics ... 37

Chapter 4 Learning to Teach/Teaching to Learn Science and Mathematics ... 63

Chapter 5 Leadership as Effective Collaborations in Science and Mathematics ..... 87

Chapter 6 Who Needs Science and Mathematics? ..... 101

Bibliography ........ 117

Index ........... 127

Teaching Secondary Mathematics as if the Planet Matters

Alf Coles, Richard Barwell, Tony Cotton, Jan Winter e Laurinda Brown

Routledge | 2013 |190 páginas | rar - pdf | 1,2 Mb

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‘This book moves us beyond a theoretical pondering of the issues and makes concrete suggestions for teachers and students for how things can be different in mathematics classrooms. This is long overdue.’
Peter Gates, University of Nottingham

Teaching Mathematics as if the Planet Matters explores how Mathematics teachers can develop approaches to curriculum and learning which help students understand the nature of the contemporary world. It sets out a model for teaching and learning that allows teachers to examine existing approaches to teaching and draw upon the insights of mathematics as a discipline to help students relate classroom mathematics to global issues such as climate change, the economy, food supplies, biodiversity, human rights, and social justice.

Including practical examples, suggestions for teaching activities and detailed further reading sections, the book covers:

• the mathematics of description in the measuring, recording and statistical analysis that informs our knowledge of climate change, consumption and sustainability;

• the mathematics of prediction in the modelling used by governments, scientists and businesses to plan roads, power stations and food supplies and their effects;

• the mathematics of communication in the news reports, blogs and environmental campaigns, incomplete without graphs, charts and statistics.

The true worth of a school subject is revealed in how far it can account for and respond to the major issues of the time. The issue of the environment cuts across subject boundaries and requires an interdisciplinary response. Mathematics teachers are part of that response and they have a crucial role in helping students to respond to environmental issues and representations.

Contents
List of figures vii
List of tables ix
Preface xi
Part I: A critical stance on global issues 1
1 The role of mathematics in shaping our world 3
Richard Barwell
2 The economy 16
Laurinda Brown
3 Climate change 31
Richard Barwell
4 Food 50
Jan Winter
5 Biodiversity 60
Alf Coles
6 Towards a mathematics for human rights and social justice 73
Tony Cotton
Part II: Into the classroom as if the planet matters 85
7 Critical mathematics education: from theory to practice 87
Tony Cotton
8 Starting from handling data 98
Tony Cotton
9 Starting from algebra 108
Alf Coles
10 Starting from number 121
Jan Winter
11 Starting from geometry 134
Alf Coles and Laurinda Brown
12 Starting from probability 148
Richard Barwell
Conclusion: the planet matters – does mathematics teaching? 162
Index 168

The Handbook of Mathematics Teacher Education: Volume1 - Knowledge and Beliefs in Mathematics Teaching and Teaching Development

Peter Sullivan e Terry Wood 

Sense Publishers | 2008 | 317 páginas | rar - pdf | 12,64 Mb 

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The Handbook of Mathematics Teacher Education, the first of its kind, addresses the learning of mathematics teachers at all levels of schooling to teach mathematics, and the provision of activity and programmes in which this learning can take place. It consists of four volumes. Volume 1 presents research and theoretically informed perspectives on Knowledge and Beliefs in Mathematics Teaching and Teaching Development. The chapters together address the "what" of mathematics teacher education, meaning knowledge for mathematics teaching and teaching development and consideration of associated beliefs. As well as synthesising research and practice over various dimensions of these issues, the volume offers advice on 'best practice' for teacher educators, university decision makers, and those involved in systemic policy decisions on teacher education. There are four sections. The first, about mathematics discipline knowledge for teaching, contains chapters on mathematics discipline knowledge from both East Asian and Western perspectives, with separate chapters addressing primary/elementary teacher education and secondary teacher education, along with a chapter on approaches for assessing this mathematics knowledge of prospective teachers. The second section describes ways of thinking about how this mathematical knowledge is used in teaching. It includes chapters on pedagogical content knowledge, on knowledge for and about mathematics curriculum structures, the way that such knowledge can be fostered with practising teachers, on a cultural analysis of mathematical content knowledge, and on beliefs about mathematics and mathematics teaching. The third section outlines frameworks for researching issues of equity, diversity and culture in teaching mathematics. The fourth section contains a description of an approach to methods of researching mathematics discipline knowledge of teachers. Together the chapters not only confirm that the knowledge that mathematics teachers need includes both mathematical and pedagogical aspects but also explore the subtlety of the various dimensions of that knowledge. There are also suggestions of the relative emphases on the respective dimensions and ways that teacher educators might support prospective and practising teachers in acquiring and developing that knowledge.

TABLE OF CONTENTS
Preface ix
Knowledge for Teaching Mathematics: An Introduction 1
Peter Sullivan
Section 1: Mathematics Discipline Knowledge for Teaching
Chapter 1: Mathematical Discipline Knowledge Requirements for Prospective Primary Teachers, and the Structure and Teaching Approaches of Programs Designed to Develop That Knowledge 13
Mike Askew
Chapter 2: Mathematical Preparation of Prospective Elementary Teachers: Practices in Selected Education Systems in East Asia 37
Yeping Li, Yunpeng Ma, and Jeongsuk Pang
Chapter 3: Discipline Knowledge Preparation for Prospective Secondary Mathematics Teachers: An East Asian Perspective 63
Li Shiqi, Huang Rongjin, and Shin Hyunyong
Chapter 4: Mathematics for Secondary Teaching: Four Components of Discipline Knowledge for a Changing Teacher Workforce 87
Kaye Stacey
Section 2: Mathematics for and in Teaching
Chapter 5: Pedagogical Content Knowledge: Useful Concept or Elusive Notion 117
Anna Graeber and Dina Tirosh
Chapter 6: The Mathematics Teacher as Curriculum Maker: Developing Knowledge for Enacting Curriculum 133
Doug Clarke
Chapter 7: Learning to Design for Learning: The Potential of Learning Study to Enhance Teachers’ and Students’ Learning 153
Ulla Runesson
Chapter 8: Beliefs about Mathematics and Mathematics Teaching 173
Helen J. Forgasz and Gilah C. Leder
Section 3: Knowledge of Equity, Diversity and Culture in Teaching Mathematics
Chapter 9: The Social Production of Mathematics for Teaching 195
Jill Adler and Danielle Huillet
Chapter 10: Development of Mathematical Knowledge and Beliefs of Teachers: The Role of Cultural Analysis of the Content to Be Taught 223
Paolo Boero and Elda Guala
Section 4: Assessment of, and Research on, Teacher Knowledge
Chapter 11: Assessment of Mathematical Knowledge of Prospective Teachers 247
Anne D. Cockburn
Chapter 12: Researching Teachers’ Mathematics Disciplinary Knowledge 273
Tim Rowland
Critical Response to Volume Chapters
Chapter 13: PCK and Beyond 301
John Mason

Key Works in Radical Constructivism - Ernst Von Glasersfeld

Marie Larochelle

Sense Publishers | 2009 | 339 páginas | rar - pdf | 1,62 Mb

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Key works on radical constructivism brings together a number of essays by Ernst von Glasersfeld that illustrate the application of a radical constructivist way of thinking in the areas of education, language, theory of knowledge, and the analysis of a few concepts that are indispensable in almost everything we think and do. Ernst von Glasersfeld's work opens a window on how we know what we know. The present work grew out of a desire to make more accessible this line of thought, to highlight its originality and consistency, and to illustrate its fecundity in the domains of cognition and learning. The first three parts of this book contain texts by Glasersfeld that outline the constructivist approach and explicate the frequently drastic reconceptualizations he has suggested. Both the last part and the postscript consist of commentaries by Edith Ackermann, Jacques Désautels, Gérard Fourez, Leslie P. Steffe and Kenneth Tobin, scholars in the fields that Glasersfeld has been concerned with. They examine a number of critical aspects pertaining to (radical) constructivism's current and future development, often tracing out paths that warrant further exploration and reflection, in particular concerning the sociopolitical dimension of knowledge. Key works on radical constructivism is intended as a reference book for researchers, educators, and students of education-and for anyone interested in grasping, or deepening their grasp of, radical constructivism's tenets, ambitions and concerns. Readers will discover in this collection of firsthand contributions the contours of a bold, contemporary debate about a most compelling current of thought. Ernst von Glasersfeld was brought up with more than one language from the very beginning. This taught him early on that the realities people think and talk about are noticeably different. He was much influenced by Silvio Ceccato, the founder of the Operational School in Italy, and then by Jean Piaget's Genetic epistemology, to which, he believes, he was able to add some details. He worked as a language analyst at the Center for Cybernetics in Milan, directed a language research project for the Us Air Force from 1962 to 1970, and then taught as professor of cognitive psychology at the University of Georgia, USA. In 1987 he retired at the age of 75 and became Research Associate at the Scientific Reasoning Research Institute of the University of Massachusetts. Throughout, his main interest was how we come to know what we know and how thought and language are linked. He has published several books in English, German, and Italian. Marie Larochelle is Full Professor at the Faculty of Education of Université Laval, Québec City. For many years, she has actively researched socioepistemological problems related to the teaching/learning of scientific knowledge. Her publications have been primarily in the fields of science education and constructivism. Her current research interests focus on how students and future science teachers figure or represent the conflicts, controversies, negotiations and socioethical issues that shape the practice of the technosciences.

CONTENTS
Preface (Ernst von Glasersfeld) vii
List of contributors ix
Acknowledgment of sources xi
INTRODUCTION: ERNST VON GLASERSFELD’S WAY OF WORLD MAKING xiii
Marie Larochelle
PART I: LEARNING, LANGUAGE, AND THE RADICAL THEORY
1. Learning as a constructive activity 3
2. Reconstructing the concept of knowledge 21
3. Facts and the self from a constructivist point of view 31
4. Signs, communication, and language 43
5. How do we mean? A constructivist sketch of semantics 55
6. On the concept of interpretation 63
7. Piaget and the radical constructivist epistemology 73
PART II: THEORY OF KNOWLEDGE
8. Aspects of constructivism: Vico, Berkeley, Piaget 91
9. The end of a grand illusion 101
10. The simplicity complex 111
11. The logic of scientific fallibility 119
12. The incommensurability of science and poetic wisdom 129
13. Farewell to objectivity 135
14. The radical constructivist view of science 143
15. Cybernetics and the theory of knowledge 153
PART III: CONCEPTUAL ANALYSES
16. Notes on the concept of change 173
17. Abstraction, re-presentation, and reflection. An interpretation of experience and of Piaget’s approach 179
18. Representation and deduction 199
19. A constructivist approach to experiential foundations of mathematical concepts 205
20. The conceptual construction of time 225
21. Anticipation in the constructivist theory of cognition 231
22. A constructive approach to ‘universals’ 241
PART IV: COMMENTS
23. Experiences of artifacts: People’s appropriations / objects’‘affordances’ 249
Edith Ackermann
24. Knowledge as representation 259
Gérard Fourez
25. A constructivist account of knowledge production as a social phenomenon and its relation to scientific literacy 267
Jacques Désautels
26. Radical constructivism and “school mathematics” 279
Leslie P. Steffe
POSTSCRIPT: THE REVOLUTION THAT WAS CONSTRUCTIVISM 291
Kenneth Tobin
References 299
Index of names 313
Index of subjects 319

Amongst Mathematicians Teaching and Learning Mathematics at University Level

(Mathematics Teacher Education, 3) 

Elena Nardi
Springer |  2008 | 349 páginas | pdf |4,7 Mb

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This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

TABLE OF CONTENTSPROLOGUE 1
CHAPTER ONE - BACKGROUND AND CONTEXT
Summary 3
1. TALUM: a general introduction 4
2. A certain type of TALUM research 6
3. The TALUM studies the book draws on 9
CHAPTER TWO - METHOD, PROCESS AND PRESENTATION
Summary 15
1. Data samples and M 16
2. The dialogic format
The Narrative Approach 18
From interview transcripts to Dialogue: an application of the Narrative Approach 24
3. Style, format and thematic breakdown of Chapters 3 – 8 29
NOTE TO READER: A RECOMMENDATION ON HOW TO READ CHAPTERS 3-8 39
CHAPTER THREE - THE ENCOUNTER WITH FORMAL MATHEMATICAL REASONING: CONCEPTUALISING ITS SIGNIFICANCE AND ENACTING ITS TECHNIQUES
Summary 41
Episodes
1. The tension between familiar (numerical, concrete) and unfamiliar (rigorous, abstract): resorting to the familiarity of number 42
2. The tension between general and particular: 48
Constructing examples 49
Applying the general to the particular 51
3. Using definitions towards the construction of mathematical arguments: Weaving the use of definitions into the construction of a mathematical argument 57
Making the fine choice between algebraic manipulation and employment of a definition 60
4. Logic as building block of mathematical arguments: reconciling with inconclusiveness 64
5. Proof by Contradiction Spotting contradiction 70
Syndrome of the Obvious 79
6. Proof by Mathematical Induction: from n to n+1 83
7. Proof by Counterexample: the variable effect of different types of counterexample 89
Special Episodes
1. School Mathematics, UK 93
2. Inequalities 102
3. Mathematical reasoning in the context of Group Theory 103
4. Algebra / Geometry 106
CHAPTER FOUR - MEDIATING MATHEMATICAL MEANING THROUGH VERBALISATION, SYMBOLISATION AND VISUALISATION
Summary 111
Episodes
0. To appear and to be: Conquering the ‘genre’ speech of university mathematics 112
1. Strings of Symbols and Gibberish – Symbolisation and Efficiency 120
Desperate juggling of axioms and random mathematics 121
To-ing and fro-ing between mathematics and language 125
2. Premature Compression:
Why is det(aIn) = an true? 134
Why is xox = xox-1 ⇒ x = x-1 true? 136
3. Visualisation and the role of diagrams 139
4. Undervalued or Absent Verbalisation and the Integration of Words, Symbols and Diagrams 151
Special Episodes
1. The Group Table 152
Out-takes
1. Typed Up 159
CHAPTER FIVE - THE ENCOUNTER WITH THE CONCEPT OF FUNCTION
Summary 161
Episodes
1. Concept Images and Concept Definition
Domineering presences (function-as-formula), conspicuous absences (domain / range) 162
The Students’ Turbulent Relationship with the Concept Definition 166
2. Relationship with Graphs: Attraction, Repulsion, Unease and Uncertainty 168
3. The Troubling Duality at the Heart of a Concept: Function as Process, Function as Object 172
Special Episodes
1. The Tremendous Function-Lookalike That is Tanx 176
2. Polynomials and the Deceptive Familiarity of Essentially Unknown Objects 177
Out-takes
1. History Relived 179
2. Evocative Terms for 1-1 and Onto 180
3. RR: A Grotesque and Vulgar Symbol? 180
CHAPTER SIX
THE ENCOUNTER WITH THE CONCEPT OF LIMIT
Summary 181
Episodes
1. Beginning to Understand the Necessity For A Formal Definition of Convergence 182
2. Beyond the ‘Formalistic Nonsense’: Understanding the Definition of Convergence Through Its Verbalisation and Visualisation – Symbolisation As A Safer Route? 185
3. The Mechanics of Identifying and Proving A Limit In Search of N 193
Identifying the Limit of a Sequence 194
Special Episodes
1. Ignoring the ‘Head’ of a Sequence 195
Out-takes
1. ≥ or > N? 199
2. Series 200
3. Continuity and Differentiability 200
CHAPTER SEVEN - UNDERGRADUATE MATHEMATICS PEDAGOGY
Summary 205
Episodes
1. Interaction / Participation
Enhancing students’ mathematical expression through interactive interrogation of their thinking 206
Building students’ understanding through ‘Socratic dialogue’ 206
Facilitating students’ realisation of their responsibility towards their own learning 207
Benefiting from the rich environment of a one-to-one tutorial 208
Students’ resistance to participatory teaching 212
Conditioning interaction effectively 212
2. Introducing, contextualising the importance of new ideas 215
3. Concept Image Construction 217
4. Abstraction/Rigor Vs Concretisation, Intuition and Exemplification Abstraction 220
Formalism
a. Fostering the significance of mathematical literacy 224
b. The fuzzy didactical contract of university mathematics 229
Numerical experiments 234
Pictures
a. The pedagogical potential, and the strongly personal nature, of pictures 237
b. Building students’ understanding of convergence through the use of visual representations 238
c. Strengthening students’ understanding of injective and surjective functions using Venn diagrams 239
d. Strengthening students’ understanding of functional properties through construction and examination of function graphs 240
e. Negotiating meanings and appropriateness of pictures as a means of strengthening students’ concept images in Group Theory 241
The ‘toolbox’ perspective 247
The skill and art in trial-and-error: making appropriate / clever choices when deciding the steps of a proof 248
Special Episodes
1. Teaching without examples 250
2. Do not Teach Indefinite Integration 251
3. Teaching of functions, process – object, polynomials 253
4. Rules of attraction 254
5. Content coverage 255
Out-takes
1. Does learning happen anyway? 255
CHAPTER EIGHT - FRAGILE, YET CRUCIAL: THE RELATIONSHIP BETWEEN MATHEMATICIANS AND RESEARCHERS IN MATHEMATICS EDUCATION
Summary 257
Episodes
1. Benefits
Benefits from using mathematics education research 258
Benefits from engaging with mathematics education research 260
2. Reflection and critique of the practices of RME – there’s something about the way you… Do Research (an evaluation of Qualitative Inquiry and conditions under which it could work for mathematicians)
a. …currently 264
b. … and other ways you could be doing it! 273
Theorise (or: on the R C Moore diagram) 276
Write up 280
Disseminate 281
Special Episodes
1. The Reviews 285
EPILOGUE 293 - POST-SCRIPT Amongst Mathematicians: Making of, Coming to be 297
Beginnings… 297
Initial proposal 299
Flash forward… 302
Back to initial planning 304
A modified proposal 304
First trials and reviews 308
BIBLIOGRAPHY 311
THEMATIC INDEX: Mathematical Topics 333
THEMATIC INDEX: Learning and Teaching 335
AUTHOR INDEX 337

A Fresh Start for Collegiate Mathematics: Rethinking the Courses Below Calculus

Nancy Baxter Hastings

 Mathematical Association of America | 2006 | 409 páginas | rar - pdf |2,8 Mb

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Each year, over 1,000,000 students take college-level courses below calculus such as precalculus, college algebra and others that fulfill general education requirements. Most college algebra courses, and certainly all precalculus courses, were originally intended to prepare students for calculus. Most are still offered in this spirit, even though only a small percentage of students have any intention of taking calculus. This volume examines how the courses below calculus might be refocused to provide better mathematical experiences for all students. This initiative involves a greater emphasis on conceptual understanding with a de-emphasizing on rote manipulation. It encourages the use of realistic applications, math modeling and data analysis that reflect the ways mathematics is used in other disciplines. It promotes the use of active learning approaches, including group work, exploratory activities and projects. It emphasizes communication skills: reading, writing, presenting and listening. It endorses the appropriate use of technology to enhance conceptual understanding, visualization, and to enable students to tackle real-world problems.The 49 papers in this volume seek to focus attention on the problems and needs of the courses and to provide guidance to the mathematics community. Major themes include: new visions for introductory collegiate mathematics, transition from high school to college, needs of other disciplines, research on student learning, implementation issues, and ideas and projects that work.

Contents
Preface  . vii
Introduction .  .1
1 The Conference: Rethinking the Preparation for Calculus, Jack Narayan and Darren Narayan . .  3
2 Twenty Questions about Precalculus, Lynn Arthur Steen . 8
Background  13
3 Who are the Students Who Take Precalculus?, Mercedes A. McGowen . . 15
4 Enrollment Flow to and from Courses Below Calculus, Steven R. Dunbar .  . 28
5 What Have We Learned from Calculus Reform? The Road to Conceptual Understanding, Deborah Hughes Hallett . . 43
6 Calculus and Introductory College Mathematics: Current Trends and Future Directions, Susan L. Ganter .46
Theme 1. New Visions for Introductory Collegiate Mathematics . . . 55
7 Refocusing Precalculus: Challenges and Questions, Nancy Baxter Hastings . . . 57
8 Preparing Students for Calculus in the Twenty-First Century, Sheldon P. Gordon . . 64
9 Preparing for Calculus and Preparing for Life, Bernard L. Madison .. 78
10 College Algebra: A Course in Crisis, Don Small . . 83
11 Changes in College Algebra, Scott R. Herriott .  . 90
12 One Approach to Quantitative Literacy: Understanding our Quantitative World, Janet Andersen .. 101
Theme 2. The Transition from High School to College . . . 109
13 High School Overview and the Transition to College, Zalman Usiskin  . 111
14 Precalculus Reform: A High School Perspective, Daniel J. Teague . . 121
15 The Influence of Current Efforts to Improve School Mathematics on the
Preparation for Calculus, Eric Robinson and John Maceli . . 129
Theme 3. The Needs of Other Disciplines . . 151
16 Fundamental Mathematics: Voices of the Partner Disciplines, William Barker and Susan L. Ganter .153
17 Skills versus Concepts at West Point, Rich West . 160
18 Integrating Data Analysis into Precalculus Courses, Allan J. Rossman . 169
Theme 4. Student Learning and Research. . .179
19 Assessing What Students Learn: Reform versus Traditional Precalculus and Follow-up Calculus, Florence S. Gordon . .. 181
20 Student Voices and the Transition from Reform High School Mathematics to College Mathematics, Rebecca Walker .  . . 193
Theme 5. Implementation . .. .211
21 Some Political and Practical Issues in Implementing Reform, Robert E. Megginson . .. 213
22 Implementing Curricular Change in Precalculus: A Dean’s Perspective, Judy E. Ackerman .. . 219
23 The Need to Rethink Placement in Mathematics, Sheldon P. Gordon  . 224
24 Changing Technology Implies Changing Pedagogy, Lawrence C. Moore and David A. Smith .. . 229
25 Preparing for Calculus and Beyond: Some Curriculum Design Issues, Al Cuoco . 235
26 Alternatives to the One-Size-Fits-All Precalculus/College Algebra Course, Bonnie Gold 249
Theme 6. Influencing the Mathematics Community . . 255
27 Launching a Precalculus Reform Movement: Influencing the Mathematics Community, Bernard L. Madison . 257
28 Mathematics Programs for the Rest-of-Us, Naomi D. Fisher and Bonnie Saunders . . 265
29 Where Do We Go From Here? Creating a National Initiative to Refocus the Courses below Calculus, Sheldon P. Gordon . 274
Ideas and Projects that Work: Part 1  . . 283
30 College Precalculus Can Be a Barrier to Calculus: Integration of Precalculus with Calculus Can Achieve Success, Doris Schattschneider . 285
31 College Algebra Reform through Interdisciplinary Applications, William P. Fox . 295
32 Elementary Math Models: College Algebra Topics and a Liberal Arts Approach, Dan Kalman . . 304
33 The Case for Labs in Precalculus, Brigitte Lahme, Jerry Morris, and Elias Toubassi  310
34 The Fifth Rule: Direct Experience of Mathematics, Gary Simundza   320
Ideas and Projects that Work: Part 2 . . 329
35 Mathematics in Action: Empowering Students with Introductory and Intermediate College Mathematics, Ernie Danforth, Brian Gray, Arlene Kleinstein, Rick Patrick, and Sylvia Svitak . . 333
36 Precalculus: Concepts in Context, Marsha Davis .  . . 337
37 Rethinking College Algebra, Benny Evans . . . 341
38 From The Bottom Up, Sol Garfunkel .  . 345
39 The Functioning in the Real World Project, Florence S. Gordon and Sheldon P. Gordon 348
40 The Importance of a Story Line: Functions as Models of Change, Deborah Hughes Hallett 352
41 Using a Guided-Inquiry Approach to Enhance Student Learning in Precalculus, Nancy Baxter Hastings . . 355
42 Maricopa Mathematics, Alan Jacobs .  . 360
43 College Algebra/Quantitative Reasoning at the University of Massachusetts, Boston, Linda Almgren Kime . . 364
44 Developmental Algebra: The First Mathematics Course for Many College Students, Mercedes A. McGowen .. . 369
45 Workshop Precalculus: Functions, Data, and Models, Allan J. Rossman . 376
46 Contemporary College Algebra, Don Small  . 380
47 Precalculus: A Study of Functions and Their Applications, Todd Swanson . . . . 386
48 Success and Failures of a Precalculus Reform Project, David M. Wells and Lynn Tilson 390
49 The Earth Math Projects, Nancy Zumoff and Christopher Schaufele . .393

Ratio and Proportion: Research and Teaching in Mathematics Teachers’ Education

(Pre- and In-Service Mathematics Teachers of Elementary and Middle School Classes)

David Ben-Chaim (The Technion-Israel Institute of Technology, Israel), 
Yaffa Keret (The Open University of Israel, Israel) 
Bat-Sheva Ilany (Beit Berl Academic College, Israel)

Sense Publishers | 2012 | 283 páginas | pdf | 4,7 Mb

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Ratio and Proportion-Research and Teaching in Mathematics Teachers' Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their specific needs. The book reports on hands-on experience in the college classes plus teachers' experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.

TABLE OF CONTENTS
Chapter 1: Introduction ... 1
PART I: STRUCTURE OF BOOK AND TEACHING MODEL 5
Chapter 2: Structure of Book... 7
Chapter 3: A Model for Teaching Ratio and Proportion Using Authentic Investigative Activities .... 13
PART II: THEORETICAL BACKGROUND 21
Chapter 4: A Mathematical Perspective of Ratio and Proportion ... 23
Chapter 5: Proportional reasoning—A psychological-didactical view ... 49
Chapter 6: Research and new approaches in pre- and
in-service mathematics teacher education ... 61
PART III: AUTHENTIC INVESTIGATIVE ACTIVITIES, INCLUDING DIDACTIC COMMENTS AND EXPLANATIONS 71
Chapter 7: Authentic investigative activities— Introduction .. 73
Chapter 8: Group 1: Introductory activities .. 83
Chapter 9: Group 2: Rate activities . 95
Chapter 10: Group 3: Ratio activities .. 125
Chapter 11: Group 4: Stretching and Shrinking: Scaling Activities .. 145
Chapter 12: Group 5: Indirect Proportion Activities ... 181
Chapter 13: Group 6: Additional Activities
for Practice and Enrichment (All topics). 195
PART IV: ASSESSMENT TOOLS 219
Chapter 14: Introduction to Assessment Tools .. 221
Chapter 15: Questionnaire: Attitude Toward Ratio and Proportion .. 225
Chapter 16: Diagnostic Questionnaire in Ratio and Proportion ... 233
Chapter 17: Assessing Research Reports and Building a Student Portfolio . 245
PART V: ANNOTATED RESOURCES AND BIBLIOGRAPHY 253
Chapter 18: Annotated Resources .... 255

Chapter 19: Bibliography ... 269

A Practical Guide to Teaching Mathematics in the Secondary School

Clare Lee, Sue Johnston-Wilder e Robert Ward-Penny

(Routledge Teaching Guides)

Routledge | 2013 | 145 páginas | rar  - pdf | 6,5 Mb

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A Practical Guide to Teaching Mathematics in the Secondary School offers straightforward advice, inspiration and support for mathematics teachers whether in training or newly qualified. Based on the best research and practice available, it offers a wide range of tried and tested approaches that succeed in secondary classrooms. Each chapter contains a wealth of tasks and ideas that allow teachers to reflect on the approaches and make plans for using them in their own classrooms, and offers ideas for lesson plans, learning activities and suggested further reading and development.

Illustrated throughout with case studies and practical insights from classroom observations and experience, this book covers key aspects of mathematics teaching, including:

• managing the class and learning environment;

• teaching the topics of mathematics;

• encouraging mathematical thinking;

• choosing and using resources;

• using multi-media technology;

• assessing work in mathematics.

A Practical Guide to Teaching Mathematics in the Secondary School is an essential companion to the core textbook Learning to Teach Mathematics in the Secondary School. Written by expert professionals, it supports you in your development of imaginative and effective lessons on a variety of curriculum topics in different teaching situations.

Contents

List of illustrations vii

Notes on contributors ix

Series editors’ introduction xi

Acknowledgements xiii

Abbreviations used xiv

Introduction 1

1 Planning mathematics lessons 3

Robert Ward-Penny and Clare Lee

■ the process of constructing a lesson plan ■ the elements that can be used ■ planning for effective starters and plenaries ■ timing and signposting ■ interrogating, evaluating and improving your plan

2 Practical Assessment for Learning 13

Clare Lee

■ the principles of Assessment for Learning ■ how to decide what your pupils will learn ■ how your pupils can recognise success ■ providing feedback ■ flexible planning

3 ICT from the front of the class 21

Ian Boote

■ using ICT at the front of the classroom ■ encouraging greater participation and exploration ■ using presentation software effectively ■ using games ■ existing online resources and the internet ■ motivation

4 Pupil-led ICT 31

Dave Miller

■ pupils exploring mathematical ideas using ICT themselves ■ virtual manipulatives ■ using real-life data ■ graphing programs ■ geometry programs ■ practical concerns associated with ICT

5 Multimedia technology 41

Chris Chisholm

■ multimedia resources and equipment ■ making videos and podcasts ■ improving literacy and team-working skills ■ data loggers ■ graphical calculators

6 Working collaboratively 51

Andrea Pitt

■ the advantages and practicalities of working collaboratively ■ the types of activity that are suitable ■ how to make choices about the size and structure of groups ■ the teacher’s role

7 Discussion and communication 61

Jenni Ingram

■ developing communication and mathematical thinking ■ how whole-class discussions can be initiated ■ creating an environment for discussion ■ setting ground rules ■ using real-world communication

8 Enquiry as a vehicle for teaching and learning mathematics 69

Mike Ollerton

■ using enquiry as part of teaching mathematics ■ the importance of an accessible start ■ the role of the teacher ■ how enquiry enables students to work independently and collaboratively ■ how progress is assessed

9 Taking mathematics outside 83

Robert Ward-Penny

■ ideas to enable your pupils to learn mathematics outside the classroom ■ planning issues ■ the kinds of activities the pupils could use ■ how noticing mathematical situations encourages your pupils to learn mathematics

10 Active and creative mathematics 93

Nick McIvor

■ the use of games as part of teaching mathematics ■ practical aspects of using games ■ how every lesson can be a story ■ using mystery to focus the pupils ■ ways of maximising engagement

11 Developing subject knowledge 103

Robert Ward-Penny

■ developing your subject knowledge ■ extending ‘higher’ by challenging your mathematical thinking ■ ‘deeper’ using external sources and historical and cross-cultural roots ■ ‘wider’ to engage and interest your pupils

12 Action research: systematic reflective action to improve practice 113

Clare Lee

■ action research as a means of solving problems encountered in teaching ■ research methodology ■ designing a project ■ putting the ideas of action research into practice to aid professional development

Websites and resources 123

References 125

Index 127

Soviet studies in the psychology of learning and teaching mathematics - Volumes 7 - 14

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to acquaint mathematics educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction in the Soviet Union. 

Volume VII - Children's Capacity for Learning Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 276 páginas | pdf 
online: ERIC

The work of El'konin, Davydov, and Minskaya reported in this volume represents a start toward the alleviation of the lack of theory-based experimental investigations of mathematics learning and teaching. 
TABLE OF CONTENTS
Introduction, Leslie Steffe
Learning Capacity and Age Level, D. B. El'konin and V. V..Davydov
Primary Schoolchildren's Intellectual Capabilities and the Content of Instruction, D. B. El'konin
Logical and Psychological Problems of Elementary Mathematics as an Academic Subject, V. V. Davydov
The Psychological Characteristics of the "Prenumerical" Period of Mathematics Instruction, V. V. Davydov 
Developing the Concept of Number by Means of the Relationship of Quantities, G. I. Minskaya 

Volume VIII - Methods of Teaching Mathematics
Steffe, Leslie P., Ed.; And Others 
1975 | 290 páginas | pdf 
online: ERIC

This volume contains four articles: Principles, Forms, and Methods of Mathematics Instruction; ; ; and Independent Work for Pupils in Arithmetic Lessons in the Early Grades
TABLE OF CONTENTS 
Introduction, Leslie  P. Steffe
Principles, Forms, and Methods of Mathematics Instruction, I. A. Gibsh 
The Relation Between Mathematics Instruction and Life, G. G. Maslova and. A. D. Semushin 
The Pupil's Activity as a Necessary Condition for Improving the Quality of Instruction, I. A. Gibsh 
Independent Work for Pupils in Arithmetic Lessons in the Early Grades, M. I. More

Volume IX - Problem Solving Processes of Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume are concerned with the instruction in problem solving of mentally retarded pupils in the auxiliary schools of the Soviet Union. Both articles in this volume describe research in problem solving and also provide concrete suggestions for improving instruction. The literature reviews contained in these articles provide us with much information on the state of research in the Soviet Union on problem solving in mathematics.
TABLE OF CONTENTS
The Solution of Complex Arithmetic Problems in Auxiliary School, K. A. Mikhal'skii 
Basic Difficulties Encountered in Auxiliary School Pupils in Solving Arithmetic Problems, M. I. Ku'mitskaya 

Volume X - Teaching Mathematics to Mentally Retarded Children
Clarkson, Sandra P., Ed.; And Others
1975 | 184 páginas | pdf
online: ERIC

The articles in this volume deal with the instruction in geometry and arithmetic of mentally retarded pupils in the Soviet Union. These pupils attend special schools, called auxiliary schools, where they are trained in content that can later be related to specific job skills. Authors of the articles have attempted to identify the specific knowledge that the pupils possess and to design more effective instructional methods for increasing that knowledge. 
TABLE OF CONTENTS
Introduction
Instructing Auxiliary School Pupils in Visual Geometry, P. G. Tishini
Visual.and Verbal Means in Pregaratory Exercises in Teaching Arithmetic Problem Solving, N. F. Kuimina-Syromyatnikova
Some Features of Elementary Arithmetic Instruction for Auxiliary School Pupils, T. V. Khanutina 

Volume XI - Analysis and Synthesis as Problem Solving Methods
Kantowski, Mary Grace, Ed.; And Others
1975 | 186 páginas | pdf
online: ERIC

This volume differs from the others in the series in that the entire volume records the search for a method of problem-solving instruction based on the analytic-synthetic nature of the problem-solving process. In this work, Kalmykova traces the history of the use of the analytic and synthetic methods in her country, explores elementary classroom situations involving teachers who had various degrees of success in problem-solving instruction, makes hypotheses regarding the use of certain techniques, and concludes with suggestions for "productive" methods to be used in the classroom
TABLE OF CONTENTS
Introduction, Mary C. Kantowski
Chapter I. Overview
Chapter II. Substantiation of the Problem of Analysis end Synthesis
Chapter III. Experimental Investigations of the Use of the Method of Analysis in School 
Chapter IV. Experimental Investigations of Analysis as a Method of Searching for a Solution
Chapter V. Productive Method of Analysis and Synthesis

Volume XII - Problems of Instruction
Wilson, James W., Ed.; And Others
1975 | 185 páginas | pdf
online: ERIC

The seven studies found in this volume are: ;; ;;; ; and Psychological Characteristics of Pupils' Assimilation of the Concept of a Function.
TABLE OF CONTENTS
Introduction
An Experiment in the Psychological Analysis of Algebraic Errors, P. A. Shevarev
Pupils' Comprehension of Geometric Proofs, F. N. Gonoboldn
Elements of the Historical Approach in Teaching Mathematics, I. N. Shevchenko
Overcoming Students' Errors in the Independent Solution of Arithmetic Problems, 0. T. Yochkovskaya
Stimulating Student Activity in the Study of Functional Relationships, Yu. I. Goldberg
Psychological Grounds for Extensive Use of Unsolvable Problems, Ya.  I.  Grudenov
Psychological Characteristics of Pupils' Assimilation of the Concept of a Function, I. A. Marnyanskii

Volume XIII - Analysis of Reasoning Processes
Wilson, James W., Ed.; And Others
1975 | 244 páginas | pdf
online: ERIC

The analysis of reasoning processes in the learning of concepts or the solving of problems is the theme common to the ten articles in this volume. These articles, except for the first one by Ushakova, were published between 1960 and 1967 and were part of the available literature during a revision of the Soviet school mathematics curriculum. The articles are interesting because of the topics they treat and because of the research styles they illustrate
TABLE OF CONTENTS
Introduction, James Wilson and Jeremy Kilpatrick
The Role of Comparison in-the Formation of Concepts do by Third-Grade Pupils,  M. N. Ushakova
On the Formation of an Elementary Concept of Number by the Child, V. V. Davydov
The Generalized Conception in Problem Solving, A. V. Brushlinskii
An Analysis of the Process of Solving Simple Arithmetic Problem, G. P. Shchedrovitskii and S. G. Yak'obson 
An Attempt at an Experimental Investigation of Psychological Regularity in Learning, B. B. Kopov
The Formation of Generalized Operations as a Method for Preparing Pupils to Solve Geometry Problems Independently, E. I. Mashbits
An Experimental Investigation of Problem Solving and Modeling the Thought Processes, D. N.Zavalishin and V. N. Pushkin 
The Composition of Pupils' Geometry Skills, A. K. Artemov
On the Process of Searching for an Unknown-While Solving a Mental Problem,  A. V. Brushlinskii
The Mechanisms of Solving Arithmetic Problems, L. M. Fridman

Volume XIV - Teaching Arithmetic in the Elementary School
Hooten, Joseph R., Ed.; And Others
1975 | 214 páginas | pdf
online: ERIC

The six chapter titles are: 
The Psychological and Didactic Principles of Teaching Arithmetic; 
The Introduction of Numbers, Counting, and the Arithmetical Operations;
Instruction in Mental and Written Calculation; Teaching Problem Solving; 
Geometry in the Primary Grades; 
Different Kinds of Pupils and How to Approach Them in Arithmetic Instruction.